Calculations at a stylized drop shape, a simple, two-dimensional drop. This is made of a circular segment with an angle between 180° and 360°, on which a fitting isosceles triangle is attached. The tangent angle at the point where the circular segment ends is equal to the angle between the legs and the base of the isosceles triangle.
Enter radius and height of the circular segment. Choose the number of decimal places, then click Calculate. The height must be larger than the radius and smaller than twice the radius, r < hs < 2r. The angle is calculated and displayed in degrees, here you can convert angle units.
Formulas:
α = 180° - arccos( 1 - hs / r)
l = r * 2 * arccos( 1 - hs / r)
c = 2 * √ 2 * r * hs - hs²
a = c / sin(180°-2*α) * sin(α)
h = hs + √ (4a²-c²)/4
p = l + 2a
A = [ r * l + c * ( hs - r ) + c * √ (4a²-c²)/4 ] / 2
Radiuses, heights, lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
This drop shape is very simplified and therefore fairly easy to calculate, as it is made up of two well-known geometric shapes. Many drawn drops are shown in this way. Sometimes drops are drawn more elongated, the lower part is then an elliptical segment. The upper part, which ends in a point, is sometimes shown curved inwards; here, for example, an interarc triangle can be used. However, no plausible transition without a kink would be possible between this and the ellipse segment; for such a transition, a sinusoidal connection can be placed between them. The calculation then becomes very complicated. It becomes even more difficult if the drop is not shown straight, but curved. Although drops normally fall straight down, wind can of course affect the symmetry of the drops. It should be noted here, however, that the stylized drop shape can differ greatly from real water drops.